## Will Luck be a Lady tonight?

August 12, 2009

The 8th August 2009 edition of  New Scientist ran an article WHAT’S LUCK GOT TO DO WITH IT? by Helen Thomson  showing the link between maths and gambling.

She tells the story of Londoner Ashley Revell who in 2004 sold his house and all his possessions , flew to Las Vegas and went straight to the roulette table and put all his money ( AUD\$ 153,680.00) on red.

Was he crazy???????

Some would say “yes”. The crowd held their breath. The ball rolled and landed on Red 7.

As with the flip of a coin there is a 50:50 chance in roulette of the ball landing on Red or Black. But the odds of 50:50 only apply over an infinite number of spins of the roulette wheel. It is possible that a roulette ball will land on Black 10, 15 or even 20 times in a row.  In fact, the highest recored run of  Black in a row was 26. (See: Mathspig The Wheel on the Roulette Table Went Round and Round )

CAN MATHS IMPROVE THE ODDS?????

In his book RISK Australian author, Max Barry, gives an insight into gambling. Here is his proposition. You start with \$10 and bet on the flip of a coin. H or T.

T: Win \$10 plus 10c.

With the odds set at 50:50 how can you lose? You must win, on average, 10c for half the throws so that over 100 throws you would win \$5 surely?

OH NO. YOU CAN LOSE BIG TIME!!!! It is possible to flip 50 Hs in a row. Then you have a big problem if, in fact, you are bankrupt at this point. In order to keep gambling you needed more than \$500. This is one of the problems with gambling. You must start with enough money to pay your way through the losing runs. If you are bankrupt you are out of the game and so you have lost all of your money.

How much money do you need in your pocket to be fairly , but not totally, sure you will not go bankrupt because then the game is over, Red Rover!

Mathspigs gather round. There is a formula called The Kelly Criterion. You can find details on Wikipedia. According to the Kelly Criterion to play this \$10 game you need to start with  ….\$2,000 otherwise there is too much risk of going broke.

You can watch Max talk about The Kelly Criterion and risk on an ABC FORA program. Start at the 19 minute mark. Watch for 5 minutes. It is a fab lecture but be warned Max talks about his father committing suicide so teacher discretion is needed, as always.

Was Ashley Revell crazy???? You work it out. According to the Kelly Criterion how much money should Ashley have had in his kitty to make sure-ish but not totally that with each bet of AUD\$ 153,680.00 he did not go broke? Make this an approximation. Use simple multiplication from the above example. But remember that in roulette the payout is double or nothing. Players DO NOT win that extra 10% sweetener so the risk of going broke is MUCH higher.